Volume 23 Issue 10/11- Publication Date: 1 October - November 2004
Special Issue on the 5th International Conference on Climbing and Walking Robots, CLAWAR 2002
Optimal Gait Synthesis of a Seven-Link Planar Biped
G. Bessonnet, S. Chessé, and P. Sardain Laboratoire de Mécanique des Solides, CNRS-UMR6610, University of Poitiers, SP2MI, Bd. M. & P. Curie, BP 30179, 86962 Futuroscope-Chasseneuil, France

In this paper, we carry out the dynamics-based optimization of sagittal gait cycles of a planar seven-link biped using the Pontryagin maximum principle. Special attention is devoted to the double-support phase of the gait, during which the movement is subjected to severe limiting conditions. In particular, due to the fact that the biped moves as a closed kinematic chain, overactuation must be compatible with double, non-sliding unilateral contacts with the supporting ground. The closed chain is considered as open at front foot level. A full set of joint coordinates is introduced to formulate a complete Hamiltonian dynamic model of the biped. Contact forces at the front foot are considered as additional control variables of the stated optimal control problem. This is restated as a state-unconstrained optimization problem which is finally recast, using the Pontryagin maximum principle, as a two-point boundary value problem. This final problem is solved using a standard computing code. A gait sequence, comprising starting, cyclic, and stopping steps, is generated in the form of a numerical simulation.

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